1.08 Identifying and evaluating algebraic expressions

Identifying components of algebraic expressions

Recall some of the components of algebraic expressions.  An expression is a representation of a quantity that may contain numbers, variables or operation symbols.  For each of the algebraic expressions below, we can identify each type of component.

Component	Algebraic expresison	Example
Variables	$x^2-x-6$x2−x−6	$x$x
Terms	$x^2-x-6$x2−x−6	$x^2$x2, $-x$−x, and $-6$−6
Constant Terms	$x^2-x-6$x2−x−6	$-6$−6
Like Terms	$x^2-x-6+3x^2$x2−x−6+3x2	$x^2$x2 and $3x^2$3x2
Coefficients	$3x^2-x-6$3x2−x−6	$3$3 is a coefficient of $x^2$x2, $-1$−1 is a coefficient of $x$x

 

Practice questions

Question 1

QUESTION 2

 

Substituting into algebraic expressions

We often want to substitute values for the variables in an algebraic expression. That way we can evaluate the expression to yield a numerical result. Let’s go through an example below.

Worked example

Question 3

Evaluate: Consider the algebraic expression $a^2+2ab-4c^2+\sqrt{a}$a2+2ab−4c2+√a. Let's evaluate this expression when $a=4$a=4, $b=3$b=3 and $c=2$c=2.

Think: Substituting $a=4$a=4, $b=3$b=3 and $c=2$c=2, the expression becomes:

$a^2+2ab-4c^2+\sqrt{a}$a2+2ab−4c2+√a

$=$=

$\left(4\right)^2+2\times\left(4\right)\times\left(3\right)-4\left(2\right)^2+\sqrt{\left(4\right)}$(4)2+2×(4)×(3)−4(2)2+√(4)

 

Do: We then need to follow the order of operations to evaluate

$a^2+2ab-4c^2+\sqrt{a}$a2+2ab−4c2+√a	$=$=	$\left(4\right)^2+2\times\left(4\right)\times\left(3\right)-4\left(2\right)^2+\sqrt{\left(4\right)}$(4)2+2×(4)×(3)−4(2)2+√(4)
	$=$=	$16+24-16+2$16+24−16+2
	$=$=	$26$26

 

Reflect: Notice how the order of operations stays the same when we are evaluating expressions.

 

Practice questions

question 4

QUESTION 5

question 6